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answered Jan 18, 2016 by TPham (5,010 points)
Maximum Allowable Working Pressure (MAWP) is the maximum gauge pressure permissible at the top of a completed vessel in its operating position for a designated temperature.  The pressure is based on calculations for each element in a vessel using nominal thicknesses, which are exclusive of additional metal thicknesses allowed for corrosion and loadings other than pressure.  The maximum allowable working pressure is the basis for the pressure setting of the pressure relief devices that protect the vessel.

Whereas Maximum Operating Pressure is the maximum pressure that equipment can be operated at below its high pressure alarm or shutdown, or 95% of MAWP, whichever is lower.